Application of generalized Lucas wavelet method for solving nonlinear fractal-fractional optimal control problems

Different types of fractional derivatives have recently been noticed by researchers and used in modeling phenomena due to their characteristics. Furthermore, fractional optimal control problems have been the focus of many researchers because they reflect the real nature of different models. Hence, this article considers a class of nonlinear fractal-fractional optimal control problems in the Atangana–Riemann–Liouville sense with the Mittag-Leffler non-singular kernel. In this study, a numerical method based on the generalized Lucas wavelets and the Ritz method is presented to obtain approximate solutions. Then, the generalized Lucas wavelets and an extra pseudo-operational matrix of the Atangana–Riemann–Liouville derivative are introduced. We demonstrate the advantage of the proposed method through three numerical examples. •We introduce a new family of wavelets named generalized Lucas wavelets.•The Lucas wavelets are a special kind of wavelet function.•These functions have two free parameters (α,β) more than other wavelets.•We proposed an extra pseudo-operational matrix of Atangana–Riemann–Liouville derivative.•Ritz method is utilized to solve nonlinear fractal-fractional optimal control problems.